The Hipparcos Catalogue as a realisation of the extragalactic reference system J. Kovalevsky, L. Lindegren, M Perryman, P Hemenway, K Johnston, V Kislyuk, J Lestrade, L Morrison, I Platais, S Röser, et al.
To cite this version:
J. Kovalevsky, L. Lindegren, M Perryman, P Hemenway, K Johnston, et al.. The Hipparcos Catalogue as a realisation of the extragalactic reference system. Astronomy and Astrophysics - A&A, EDP Sciences, 1997, 323, pp.620-633. hal-02053947
HAL Id: hal-02053947 https://hal.archives-ouvertes.fr/hal-02053947 Submitted on 1 Mar 2019
HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Astron. Astrophys. 323, 620–633 (1997) ASTRONOMY AND ASTROPHYSICS
The Hipparcos Catalogue as a realisation of the extragalactic reference system
J. Kovalevsky1, L. Lindegren2, M.A.C. Perryman3, P.D. Hemenway4, K.J. Johnston5, V.S. Kislyuk6, J.F. Lestrade7, L.V. Morrison8, I. Platais9,S.Roser¨ 10, E. Schilbach11, H.-J. Tucholke12, C.deVegt13, J. Vondrak´ 14, F. Arias15, A.M. Gontier16, F. Arenou7, P. Brosche12, D.R. Florkowski5, S.T. Garrington17, R.A. Preston18, C. Ron14, S.P. Rybka6, R.-D. Scholz11, and N. Zacharias5 1 CERGA, Observatoire de la Coteˆ d’Azur, Av. Copernic, F-06130 Grasse, France 2 Lund Observatory, Box 43, S-22100 Lund, Sweden 3 Astrophysics Division, European Space Agency, ESTEC, Noordwijk 2200 AG, The Netherlands 4 Astronomy Dept., University of Texas, RLM 15308, Austin, TX 78712 1083, USA 5 US Naval Observatory, 3450 Massachusetts Ave NW, Washington DC, 20392, USA 6 Main Astron. Observatory Ukrainian Ac. Sc., Goloseevo, 252127 Kiev, Ukraine 7 Observatoire de Paris, Section de Meudon, F-92195 Meudon Principal Cedex, France 8 Royal Greenwich Observatory, Madingley Road, Cambridge CB3 0EZ, UK 9 Yale University Observatory, PO Box 208101, New Haven CT 06520-8101, USA 10 Astronomisches Rechen-Institut, Monchhofstrasse¨ 12–14, D-69120 Heidelberg, Germany 11 WIP, Universitat¨ Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany 12 Universitats¨ Sternwarte, Auf dem Hugel¨ 71, D-53121 Bonn, Germany 13 Hamburger Sternwarte, Gojensbergsweg 112, D-21029 Hamburg, Germany 14 Astronomical Institute, Bocnˇ ´ı II 1401, 14131 Prague 4, Czechien 15 Observatorio Astronomico, Paseo del Bosque, S/N, 1900 La Plata, Argentina 16 IERS, Observatoire de Paris, 61, avenue de l’Observatoire, F-75014 Paris, France 17 University of Manchester, NRAL, Jodrell Bank, Macclesfield, Cheshire SK11 9DL, UK 18 Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
Received 15 October 1996 / Accepted 8 November 1996
Abstract. The paper describes the methods and observations vations. The methods give very similar solutions, and a mean by which the Hipparcos Catalogue was linked to the Interna- value was adopted for the definition of the system of positions tional Celestial Reference System (ICRS). The contributions of and proper motions in the Hipparcos Catalogue. As a result, several groups represented in the authorship of this paper, us- the coordinate axes defined by the published catalogue are be- ing a variety of techniques, were synthesised in order to deter- lieved to be aligned with the extragalactic radio frame to within mine the global orientation and rotation (spin) of the coordinate ±0.6 mas at the epoch 1991.25, and non-rotating with respect frame defined by the Hipparcos data with respect to extragalac- to distant extragalactic objects to within ±0.25 mas/yr. tic sources. The following link techniques were used: interfero- metric observations of radio stars by VLBI networks, MERLIN Key words: astrometry – catalogs – reference systems and VLA; observations of quasars relative to Hipparcos stars by means of CCDs and photographic plates, and by the Hubble Space Telescope; photographic programmes to determine stel- lar proper motions with respect to extragalactic objects (Bonn, Kiev, Lick, Potsdam, Yale/San Juan); and comparison of Earth 1. Introduction orientation parameters obtained by VLBI and by ground-based optical observations of Hipparcos stars. Although vastly dif- The Hipparcos and Tycho Catalogues are now completed and ferent in terms of instruments, observational methods and ob- will be generally available to the astronomical community in jects involved, the various techniques generally agree to within mid-1997 (ESA 1997). They are the result of an immense effort 10 mas (milliarcsec) in the orientation and 1 mas/yr in the spin not least on the part of the various scientific ‘consortia’ charged of the system. Two different numerical methods are described with the preparation of the observing programme and the deriva- for the systematic comparison and synthesis of the link obser- tion of astrometric and photometric parameters from the satel- lite data: the Input Catalogue Consortium, INCA (Turon et al. J. Kovalevsky et al.: The Hipparcos Catalogue as a realisation of the extragalactic reference system 621
1992), and the data reduction consortia FAST, NDAC and TDAC state of the provisional data in H37C. Instead, this paper gives (Kovalevsky et al. 1992, Lindegren et al. 1992, Høg et al. 1992). consistently the differences between these values and the final Linking the satellite results to an extragalactic reference sys- set of adopted values. The rotation parameters reported below tem represents an additional and considerable effort, involving consequently describe the results of the link observations as a wide range of observational techniques both from the ground if they had been analysed with respect to the final Hipparcos and from space. It is the purpose of this paper to describe these Catalogue. Also, the adopted results of the synthesis, as given techniques and their main results, and to explain how the results in Sect. 5, are identically zero. were synthesised in order to define the coordinate axes for the The purpose of the link is to put the Hipparcos and Tycho system of positions and proper motions in the Hipparcos and Catalogues on a reference frame which corresponds as closely Tycho Catalogues. as possible to the extragalactic frame realised over the past Hipparcos was able to measure very accurately the angles decades through the extremely accurate VLBI observations of between objects on its observing list. From these angles, and radio sources. their variation in time, the positions and proper motions of the The importance of this link was stressed already in the stars could be calculated in a single coordinate system cover- planning of the observing programme for Hipparcos. Extensive ing the whole sky, and their absolute trigonometric parallaxes preparations were made by the INCA Consortium, within the were obtained at the same time. However, because practically framework of major collaborative programmes, to initiate and no extragalactic objects were observed (due to the limiting mag- collect relevant ground-based observations of radio stars and nitude of V ∼ 12.3), the resulting coordinate system was es- stars in the fields of compact extragalactic radio sources, and to sentially free to spin slowly with respect to distant galaxies, and ensure that suitable link stars were included on the observing list. the precise orientation of its axes at a given instant was also un- Various techniques for link observations were considered (radio defined by the observations. The data reductions thus resulted observations by VLBI, MERLIN and VLA; ground-based as- in preliminary versions of the Hipparcos and Tycho catalogues, trometry; speckle interferometry; Hubble observations with the in which the positions and proper motions were expressed in a FGS) and have been described in some detail in Argue (1989; very well-defined, but to some extent arbitrary, reference frame. see also Argue 1991 for an update). In parallel, the suitability This provisional frame was in practice fixed by the special pro- of the selected link stars for measurement by Hipparcos and for cedure by which the main FAST and NDAC astrometric results consistency with the radio model were performed. Link condi- were merged into a single provisional catalogue called H37C. tions were first simulated by Frœschle´ and Kovalevsky (1992) The positions and proper motions in the Hipparcos Catalogue and then other tests were made using simulations of the mission were obtained by applying a rigid-body rotation of the coordi- and, in some cases, the observing programme was modified in nate frame in H37C. This rotation was defined by six numbers: order to obtain a satisfactory observing time on each of the radio three of them represent the orientation offset of H37C about the and Hubble link stars (Turon et al. 1992). principal equatorial axes at the catalogue epoch J1991.25 (ε0x, Meanwhile, the IAU adopted a resolution (Bergeron 1992) ε0y, ε0z); the other three give the rates of change in time of the stating that the next celestial reference system should be based orientation offset, or the spin of H37C with respect to the final upon positions of extragalactic radio sources, but that it will frame (ωx, ωy, ωz). The Tycho Catalogue was later aligned with come into effect only when there is a realisation of the system the Hipparcos Catalogue by a similar process, based on a direct in the optical domain. It was then understood that this realisa- comparison of the positions and proper motions of the common tion should be the Hipparcos Catalogue, given its expected high stars (which included nearly all the Hipparcos stars). precision and extension to more than a hundred thousand stars. The precise definition of the orientation and spin vectors In 1993 the Hipparcos Science Team appointed a working were given in a previous paper (Lindegren & Kovalevsky 1995). group for the determination of the extragalactic link, continuing The equations of condition for determining these vectors from and extending the preparatory work of the INCA Consortium. different kinds of link observations were also given. Following The composition of the working group has varied somewhat, the main principles and conventions of that paper, the link obser- but when the final link results were computed in early 1996, the vations were analysed with respect to the positions and proper 14 first authors of this paper had the main responsibility for the motions in H37C by the various groups represented in the au- different link techniques and for the evaluation and synthesis of thorship of the present paper and further described in Sect. 3. the results. Each group thus provided an estimate of the orientation and/or The quality of the final link is a function of three factors: spin of H37C with respect to the extragalactic frame, and these 1. The uncertainties of the proper motions of the Hipparcos estimates were then compared and synthesised as described in Catalogue. Because the results for double stars are subject to Sect. 4 and 5. The end result of this process was an adopted greater errors, only apparently single stars were used for the set of orientation and spin components, which was applied to link with the exception of VLBI for which a double star model H37C in order to produce the reference frame of the published was provided for two radio-sources. The average standard errors Hipparcos Catalogue. of these stars, if brighter than V = 9 mag, are 0.8 mas and The actual values of the orientation and spin components 0.9 mas/yr for the components of position (at epoch J1991.25) found by the various groups and by the synthesis methods are not and proper motion; for 11 ≤ V ≤ 12 the typical standard errors given in this paper, as they merely reflect the arbitrary rotational are, respectively, 2.1 mas and 2.6 mas/yr. 622 J. Kovalevsky et al.: The Hipparcos Catalogue as a realisation of the extragalactic reference system
200
150
100 Number of sources
50
0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Fig. 2. Sky distribution of radio stars used for the link by VLBI (squares) Uncertainties in α cos δ and δ (mas) and MERLIN (asterisks) Fig. 1. Histogram of uncertainties (standard errors) achieved for the 253 radio positions in ICRF for the defining radio-sources and all sources used for Hipparcos link. Full line: right ascensions; dotted line: decli- new reference system replacing the FK5 system. The Hipparcos nations and Tycho Catalogues will be its first realisation for optical astronomy. It should be noted that the orientation of the Hipparcos Cat- 2. The uncertainties of the extragalactic reference frame alogue is fixed to the ICRF using direct links between the po- used for setting the origin of the catalogue. This frame is dis- sitions of Hipparcos stars at the catalogue epoch J1991.25 and cussed in the next section. radio sources in the ICRF itself. The time-dependent rotation 3. The actual errors and uncertainties of other references (spin), on the other hand, is fixed by linking the Hipparcos proper used and of the link observations connecting the two reference motions to any external sources, such as galaxies, which are not frames. These are different for each method, as presented in necessarily included in the ICRF. Sect. 3. • In practice we shall show that the limiting factors presently affecting the reference frame link are the number and accuracy 3. Individual link solutions of the positions and proper motions of the non-Hipparcos obser- In the following subsections, the various methods used for the vations. These may be improved in the future with acquisition link are described individually. They are presented in the fol- of new observations of Hipparcos stars in the extragalactic ref- lowing order: erence frame. 1. Radio and optical techniques providing high-precision po- sitional links to a small number of Hipparcos stars. These 2. The international celestial reference system define the orientation parameters ε0 very accurately, but con- ω Since 1988, the International Earth Rotation Service (IERS) has tribute less to the determination of the spin ( ) due to the implemented and maintained an extragalactic reference frame small number of objects and the relatively short time span containing an increasing number of extragalactic radio sources of the observations. observed by several VLBI networks throughout the world. At 2. Use of proper motion surveys where the motions of large the request of the IAU working group on reference frames, IERS numbers of stars are measured relative to galaxies. These ω finalised this iterative process and provided a definitive list of only contribute to the determination of . objects and coordinates in October 1995. 3. Special photographic link programmes. The final catalogue is the International Celestial Reference 4. Use of Earth orientation parameters. Frame (ICRF) of 610 sources uniformily distributed on the sky. The numerical results of the individual link solutions, expressed The J2000.0 VLBI coordinates of these sources materialize the as residuals with respect to the adopted global solutions, are International Celestial Reference System (ICRS, Arias et al., given in Table 3. 1995). In order to provide radio-source coordinates to link Hip- parcos reference frame to the ICRS, a subset of this catalogue 3.1. VLBI observations that contains 212 defining sources and all sources used for Hip- parcos link was issued. Fig. 1 gives the distribution of accuracies Multi-epoch VLBI observations were conducted between 1984 achieved on these subset of 253 sources. More details are to be and 1994 to determine the positions, proper motions and paral- found in Ma et al. (1997). The coordinates of these sources are laxes of 12 radio-emitting stars. Their positions on the sky are given in IERS (1996). shown by the squares in Fig. 2. As a result of the present link, all the coordinates published The observations were conducted on the US VLBI Network, in the Hipparcos and Tycho Catalogues are referred to the ICRS. NASA Deep Space Network, NRAO VeryLarge Baseline Array It is expected that in 1997 the IAU will approve ICRS as the (VLBA) and European VLBI Network. The data processing and J. Kovalevsky et al.: The Hipparcos Catalogue as a realisation of the extragalactic reference system 623 analysis is described in Lestrade et al. (1995). All the VLBI ob- Table 1. Uncertainties of the absolute positions (at epoch J1991.25), servations for each star were phase-referenced to an angularly proper motions and trigonometric parallaxes of the 12 link stars as nearby extragalactic radio source on the ICRF list. The result- determined by VLBI observations ing uncertainties in the astrometric parameters are presented in Table 1. The standard errors of the relative positions between Hipparcos Standard errors number Star name Pos. P.M. Par. extragalactic reference sources and the radio stars are all smaller (HIP) (mas) (mas/yr) (mas) than 1 mas, but uncertainties in the IERS coordinates of the ref- erence sources make the standard errors in absolute position for 12 469 LSI 61◦303∗ 3.0 0.30 0.62 the stars usually larger than 1 mas. 14 576 Algol 0.61 0.18 0.59 The six components of ε0 and ω were simultaneously solved 16 042 UX Ari 2.1 0.20 0.39 by a least squares fit as described in Lestrade et al. (1995), using 16 846 HR 1099 0.48 0.31 0.47 weights based on the combined VLBI and Hipparcos a priori 19 762 HD 283 447 3.0 0.28 0.25 measurement uncertainties. This led to a chi-square goodness of 23 106 HD 32 918 1.5 1.00 0.80 fit of 56, with 42 degrees of freedom. Subsequently, two objects 66 257 HR 5110 1.28 0.16 0.45 79 607 σ2 CrB 0.29 0.05 0.10 were down-weighted by increasing their positional uncertainties ∗∗ 98 298 Cyg X1 1.50 0.14 0.30 by a factor of 3: for HIP 12 469 (LSI 61◦303) because of its jet 103 144 HD 199 178 1.95 0.43 0.33 structure on a 10 mas scale, and for HIP 19 762 (HD 283 447) 109 303 AR Lac 0.94 0.19 0.37 because of its known duplicity on a scale of ' 0.1 arcsec (Ghez 112 997 IM Peg 1.42 0.47 0.68 et al. 1993) which is difficult for Hipparcos. No modifications had to be applied on the a priori proper motion uncertainties. ∗ V615 Cas ∗∗ V1357 Cyg After this adjustment of the weights, the chi-square goodness of fit became a satisfactory 36, with 37 degrees of freedom. Further tests were done by splitting the 12 stars in various HIP 16 879 (HD 22 403), HIP 19 431 (HD 26 337), HIP 53 425 subsets. This showed that the fit is quite robust: for instance, (DM UMa), HIP 65 915 (FK Com), HIP 85 852 (29 Dra), the differences between the fits of two independent subsets of HIP 91 009 (BY Dra), HIP 108 644 (FF Aqr), HIP 116 584 six stars each were within the combined uncertainties (less than (λ And) and HIP 117 915 (II Peg). These stars have flux densi- 1 mas for the orientation components and less than 0.6 mas/yr ties of between 2 and 12 mJy which is weaker than those used for the spin components). The formal standard errors are very for VLBI observations. Their positions are shown by the aster- similar in all three axes, viz. 0.5 mas for the components of isks in Fig. 2. ε0 and 0.3 mas/yr for the components of ω. The rms post-fit The positions of individual stars, relative to the ICRF residuals are, respectively, 1.72 mas and 0.84 mas/yr. sources, are estimated to have individual errors of approximately J.F. Lestrade has led the project in close collaboration with 4 mas. This includes ‘noise’ in the determination of the cen- R.A. Preston, D.L. Jones (JPL) and R.B. Phillips (Haystack) troid of the weak radio star image and various calibration errors, for the northern stars, and J. Reynolds, D. Jauncey (CSIRO) which are proportional to the separation of the star and calibrator and J.C. Guirado (JPL) for the southern hemisphere. and were estimated using observations of pairs of calibrators. The error estimates were confirmed by splitting the data into subsets of sources wherever possible. 3.2. Observations with MERLIN Two observations of HIP 16 879 (HD 22 403) were rejected MERLIN is a real-time radio-linked radio interferometer array because they were of poorer quality than the third; all the ob- with a maximum baseline of 217 km, giving a resolution of ap- servations of HIP 85 852 (29 Dra) were also rejected because proximately 40 mas at 5 GHz. A general description of MER- they showed a relatively bad goodness of fit in the Hipparcos re- LIN is given by Thomasson (1986) and a detailed discussion of ductions. The double star HIP 79 607 (σ CrB) was not included the observations and procedures used here is being presented because the Hipparcos observations required special treatment elsewhere (Garrington et al. 1997). and a final position was not made available to the MERLIN As in the VLBI observations described above, the positions group at the time of the analysis. So, in total, observations of 11 of weak radio stars were obtained by using ICRF sources as radio stars by MERLIN were used to link Hipparcos to the ICRF. phase calibrators. Observations were made at 4993 MHz with Three of these stars are common to the VLBI list (HIP 12 469, a bandwidth of 15 MHz. Typically, the star-calibrator sepa- 14 576, 66 257). ration was 5◦ and the cycle time was 5 to 10 min. Four of Algol is a triple system, AB–C, where the separation of AB is the brighter radio stars common to the list observed by VLBI ∼ 4 mas and AB–C is ∼ 95 mas. The Hipparcos position is the were observed in 1992. These were: HIP 12 469 (LSI 61◦303), centre of mass of the AB–C system. The radio emission comes HIP 14 576 (Algol), HIP 66 257 (HR 5110) and HIP 79 607 (σ2 from AB, so the MERLIN position was reduced to the centre CrB). In order to select an independent set, a survey of 25 of mass using the orbital elements and mass ratios given by Pan RS CVn and chromospherically active stars with a known his- et al. (1993). However, there is evidence from the Hipparcos tory of radio flaring was carried out in 1995. Astrometric ob- observations that the line of nodes in Pan et al. is wrong by 180◦. servations were then made of nine stars which were detected: The subsequent residuals for the MERLIN position of Algol 624 J. Kovalevsky et al.: The Hipparcos Catalogue as a realisation of the extragalactic reference system in this paper confirm this. With this alteration, the computed dimensional gaussian function was fitted to the stellar emission, corrections from AB to the centre of mass at the epoch of the and the centre of the gaussian was taken to be the star’s position. MERLIN observation (1993.00) were found to be +12.9 mas The stellar positions (in the extragalactic reference frame) and −10.0 mas in right ascension and declination, respectively. were moved to the epoch J1991.25 by means of the proper mo- The Hipparcos proper motions and parallaxes were used tions and parallaxes in H37C. The differences between the radio to reduce the MERLIN geocentric positions to the barycentre and Hipparcos positions were then used to solve for the orien- and catalogue epoch of Hipparcos, which is J1991.25. For the tation vector ε0. The standard error in each component of the 1995 observations, the uncertainties from the Hipparcos proper vector was about 5 mas. motions are comparable to the MERLIN position errors. The MERLIN and Hipparcos positions were subtracted and the usual 3.4. Optical positions of compact sources unweighted observational equations (see, for example, Linde- gren & Kovalevsky 1995) for the three orientation angles were The Hamburg/USNO reference frame programme has been de- solved by least-squares. scribed in Johnston et al. (1995), Ma et al. (1990), and Zacharias The solution for ε gives standard errors of 2.2 to 2.6 mas & de Vegt (1995), and the reader is referred to these publica- in the components. Compared with the VLBI solution which is tions for details. The programme is aimed at the determina- virtually independent, there is a close agreement which lends tion of precise optical and radio positions of about 400 to 500 confidence to the stability of the link which could have been selected compact radio sources which display optical counter- distorted by significant offsets between the optical and radio parts, mostly QSOs and BL Lac’s, within a visual magnitude emission of some of the binary stars. range of 12 to 21. Optical positions in the Hipparcos reference The team which worked on this project comprised frame are obtained via a system of secondary reference stars in S.T. Garrington and R.J. Davis (NRAL, Jodrell Bank), the magnitude range 12 to 14. The procedure thus requires two L.V. Morrison, R.W. Argyle (RGO), and A.N. Argue (IoA, steps: first the establishing of the secondary reference positions Cambridge). by means of astrograph plates, and then the observation of the radio sources with respect to the secondary frame by means of 3.3. Observations with VLA larger telescopes. The secondary frame was established using wide field (∼ The procedures outlined in Florkowski et al. (1985) were fol- 5◦) astrographs in both hemispheres: the yellow lens of the lowed. Observations of radio emitting stars were made with USNO 8-inch twin astrograph (South), the Hamburg astrograph, the Very Large Array (VLA) operated by the National Radio and the yellow lens of the Lick Carnegie astrograph with 3◦ ×3◦ Astronomy Observatory. The astrometric measurements were plates. All radio source fields were taken with Kodak 103aG made when the VLA was in the high resolution A configura- emulsion and a Schott filter for short-wavelength cutoff. The tion where the baseline lengths ranged from 1–36 km. A typical spectral range used was only 600 to 800 A˚ wide (centred at synthesised (half-power) beam was about 0.4 arcsec. The ob- about 5400 A),˚ thus providing a minimum influence of atmo- servations were made between March 1982 and August 1995. spheric dispersion and residual colour aberrations of the optics. As the stellar continuum flux density is weak, typically only a For each field, four plates centred on the source position were few mJy, the observations were made at C Band (6 cm) with a taken and measured in two orientations on the CCD-camera bandpass of 100 MHz. The observations were made in a differ- based Hamburg astrometric measuring machine. The measure- ential fashion with respect to an unresolved extragalactic radio ments included all Hipparcos stars in the whole plate field (typ- source. In order to minimise atmospheric noise, the phase ref- ically 50 to 100 stars), and secondary reference stars selected erence source was always within 15◦ of the star. Observations from the HST Guide Star Catalog in the central 1◦ field. The were made over a number of widely spaced hour angles in or- resulting precision of the secondary reference star catalogue is der to minimise atmospheric effects. The data from the quasar 60 to 80 mas for the individual positions based on four plates were employed to normalise the antenna gains and phases for each. The astrograph plate solutions, based on the Hipparcos the stellar radio source. The quasar 1328+307 (3C286) was used positions, reached a typical mean unit weight error of 60 to as a primary flux density calibrator. 70 mas, or 0.6 to 0.7 µm on the plate. Formally, the Hipparcos Images of the sky near the stellar radio emission were cre- reference frame could therefore be transferred locally to each ated using the Astronomical Image Processing System (AIPS). radio source field with a precision better than 10 mas. They were made with a cell size of 0.1 arcsec and in order to Optical source positions were then obtained using plates maximise the angular resolution of the image, uniform weigh- from Schmidt telescopes and the prime focus of large telescopes ing and no taper were applied to the visibility data. The maps in both hemispheres; recently also CCD frames from KPNO and were cleaned using the array processor version of CLEAN de- CTIO 90 cm telescopes were obtained (Zacharias & de Vegt vised by Clark (1980). The images of the region around the stars 1995; de Vegt & Gehlich 1982). Plate or CCD solutions were were not very complicated, and the enhanced sidelobes did not obtained using the secondary reference star catalogue. The pre- cause any difficulties in cleaning the images. Since we are inter- cision of the optical source positions based on several plates ested in the absolute phase centre of the map, self-calibration, and/or CCD frames is better than 30 mas in each case. The pro- commonly used to improve maps, was not used here. A two- gramme therefore provides optical positions of the extragalactic J. Kovalevsky et al.: The Hipparcos Catalogue as a realisation of the extragalactic reference system 625 reference frame sources in the Hipparcos frame, and the deter- data collection and analysis was the result of continued efforts mination of a precisely defined rotation between both systems of P.D. Hemenway, E.P. Bozyan, R.L. Duncombe, A. Lalich, is feasible. The presented preliminary solution is based entirely B. MacArthur, E. Nelan and the Hubble Space Telescope Team. on CCD frames of 78 globally selected sources at mean epoch 1988.5. The full program will be based on about 400 sources and 3.6. Use of the Lick proper motion programme will determine the orientation parameters on the 1 mas accuracy level. The published Part 1 of the Lick Observatory Northern Proper Motion program (NPM), also known as NPM1 (Klemola et al. 3.5. Observations with the Hubble Space Telescope 1987 and 1994), contains 149 000 stars from 899 NPM fields north of δ = −23◦ for which the proper motions have been The Fine Guidance Sensors (FGSs) of the Hubble Space Tele- determined relative to background galaxies. The mean number scope (HST) have been used to measure the angular separation of galaxies per field is 80. The typical accuracy of the NPM1 of Hipparcos stars from extragalactic objects. If the positions of absolute proper motions is 5 mas/yr. the extragalactic sources are known from VLBI observations, In total 13 455 stars are common between the NPM1 cata- the orientation of the Hipparcos frame can be determined from a logue and the Hipparcos Catalogue. Preliminary comparisons set of such measurements. If the measurements are spread over of proper motions in H37C and the NPM1 indicated a linear a sufficient interval in time, also the spin of the Hipparcos frame magnitude equation of about 1 mas yr−1 mag−1 in the NPM1 can be determined. data essentially down to the magnitude limit of the Hipparcos The FGSs measure relative positions of targets within the Catalogue. The magnitude equation is coordinate-independent, instrumental reference frame to a precision of a few milliarc- although in declination it shows a different slope for stars north sec (Benedict et al. 1992). Because of inaccuracies of the guide and south of δ = −2.5◦. It should be noted that due to the lack stars, and uncertainties of the locations of the instruments on of measurable multiple grating images in the same exposure, board HST with respect to each other, the absolute orientation it is impossible to eliminate the magnitude equation internally. of the spacecraft on the sky is unknown at the milliarcsec level Furthermore, there are no absolute proper motions available within the Astrometric FGS field of view. Therefore, the separa- which could readily be used to correct the magnitude equation tion of two objects is the most accurate datum available for the externally. Since the rotation parameters are correlated with the frame tie work. 78 separations of 46 Hipparcos stars next to 34 magnitude equation, the Hipparcos data cannot be used to cor- extragalactic objects were measured from April 1993 through rect the magnitude equation as part of the link solution. December 1995. GaussFit, a non-linear least-squares package Whatever the reason may be for the magnitude equation for (Jefferys et al. 1988), was used to determine the orientation and the fairly bright Hipparcos stars (e.g. grating image blending, spin parameters from these data. instrumental effects), extensive tests have shown that the NPM1 O − C residuals for the separations (with ‘observed’ data O catalogue is relatively free of systematic errors for the stars with coming from the HST, and ‘computed’ data C from the Hippar- mB > 12 mag on which the galactic structure and kinematic cos positions for the epoch of the HST observations combined studies are based. with the ICRF positions) showed an initial rms of 30 mas. Ap- Two different groups have independently undertaken the plication of a time-variable field distortion calibration to the task to use the NPM1 catalogue in an attempt to contribute FGSs brought the rms down to 10 mas. Application of the ac- to the link of the Hipparcos Catalogue to the extragalactic ref- curate Hipparcos parallax values brought the rms to 8 mas. The erence system. Because the two groups obtained significantly GaussFit program allowed rigorous application of the gener- different results, their separate reports are presented below. Both alised least-squares method, requiring the Hipparcos data, the groups have benefited from discussions with R.B. Hanson and VLBI data, and the HST data all to be treated as observables A.R. Klemola of the Lick Northern Proper Motion programme. with their own attendant errors. The major sources of error are Fig. 3 gives the distribution of link stars in the Lick as well the HST data (estimated at 3 to 4 mas for a single separation as the Yale/San Juan (SPM) programmes. measurement) and the propagation of the Hipparcos proper mo- tion errors to the epochs of the HST observations. One source 3.6.1. The Yale solution pair with marginally significant residuals was dominating the solution for one of the axis rotations because of its particular With regard to the magnitude equation described above, af- location with respect to the solution, and was rejected. Sev- fecting the bright NPM1 stars, three possible solutions to the eral other HST observations were rejected for various reasons problem emerge. Firstly, one may use in the solution only the including large telescope drift, large observational scatter, and relatively faint stars (e.g. mB > 10.5 mag), anticipating that inability to lock onto an extragalactic object because it was ex- the magnitude equation vanishes at some magnitude. A set of tended. A time-variable scale factor in the FGS was also found link calculations at different magnitude cutoffs showed that the from our data, and was fitted in the solution. The details will be solution improves when it is limited to fainter stars. However, published by Hemenway and his co-investigators. it cannot be concluded with confidence at which magnitude the Based on observations with the NASA/ESA Hubble Space effect disappears. Secondly, despite the correlations it seems Telescope, this work was carried out by many people, but the feasible to supplement the conventional link equations with a 626 J. Kovalevsky et al.: The Hipparcos Catalogue as a realisation of the extragalactic reference system
+90o Table 2. Results of the Heidelberg solutions for the components of the spin vector ω (in mas/yr) using the Lick NPM1 proper motions. The first line gives the solution without magnitude limits for the selection of stars; subsequent lines give the results for stars in certain intervals of the Lick (mB ) or Hipparcos (Hp) magnitude. The last line gives the o o 180 -180 formal standard errors for the solution with 1135 stars
Magnitude Number Spin components range of stars ωx ωy ωz
(no limit) 9236 −0.70 −0.27 −2.14 -90o 10.5
Previous investigations in fields with globular and open clus- sensitive to the terrestrial reference frame, and almost entirely ters (Kharchenko & Schilbach 1995, Scholz & Kharchenko insensitive to the celestial reference frame. Universal time UT1 1994) showed that systematic, magnitude-dependent errors is a special case: it is sensitive to both the celestial and terrestrial could affect the proper motions of bright stars measured on Taut- reference frames used by the two observational techniques. This enburg plates. Indeed, a simple test computing the spin param- makes the determination of ε0z impossible, as the unknown dif- eters ωx, ωy, ωz with bright (mB ≤ 9.1) and faint (mB > 9.1) ference ∆λ between the two terrestrial frames in longitude is link stars yielded significantly different results for these groups. a non-removable part of the difference in UT1 as measured by The influence of the magnitude effect was studied by succes- the two techniques. sively omitting the bright stars from the solution. It was found For the arbitrary epoch t, the formulae for calculating the that the solution became stable with stars fainter than 8.9 mag. components of the orientation vector ε from the two sets of EOP Using 256 Hipparcos stars (mB ≥ 9.0) for the link, the final read: determination of the spin vector yields formal uncertainties of 0.5 mas/yr on the components of ω. The rms residual in the εx = ∆VLBI − ∆Hip proper motions of stars is 6.9 mas/yr. The reduction procedure εy =(∆ψHip − ∆ψVLBI) sin and data analysis applied in the Potsdam solution will be de- ε + ∆λ =15.041(UT1Hip − UT1VLBI) , (1) scribed in detail in a separate paper (Hirte et al. 1997). z where is the obliquity of the ecliptic. Assuming a linear varia- ∆ 3.11. Comparison of Earth Orientation Parameters tion with time, the angles ε0x, ε0y, ε0z + λ can be determined for the reference epoch t0 while the spin components are ob- The Earth Orientation Parameters (EOP) as determined by op- tained as ωi =˙εifor i = x, y, z. Practical tests with ωz however tical astrometry and VLBI were used to obtain an indirect link proved that this method yields an improbably large value for that of the Hipparcos coordinate system to the extragalactic system. parameter, very probably due to a non-zero value of ∆λ˙ (drift In this method the terrestrial reference system (rigidly tied to of both terrestrial reference frames in longitude). Thus only the the rotating Earth) is used as an intermediary whose orientation x and y components of ε0 and ω were determined. with respect to both the Hipparcos catalogue (by optical astrom- A detailed description of the method and the results is given etry) and extragalactic objects (by VLBI) has been monitored in Vondrak´ et al. (1997). quasi-simultaneously during a decade. VLBI determines five EOP at roughly 5-day intervals; they 4. Discussion of the individual results are the components of polar motion x, y (giving the position of the celestial ephemeris pole in the terrestrial system), the The problem which had to be solved was to use all the results celestial pole offsets ∆, ∆ψ sin (giving the displacement of provided by the techniques described in the previous section the actual spin axis of the Earth from its ephemeris position in order to derive the single set of rotation parameters (εx, εy, in obliquity of the ecliptic and in longitude ψ) and the dif- εz, ωx, ωy, ωz) which best represents them all. The individual ference between Universal and Atomic time UT1–TAI (giving results are summarised in Table 3 and presented graphically in the angle between the actual zero meridian and its expected po- Fig. 4 and 5. sition assuming the uniform speed of rotation), all referred to The zero points for the data in Table 3 and Fig. 4 and 5 (and extragalactic objects. also in Table 2) have been shifted by the vectors representing The same five EOP, referred to the celestial optical system the adopted solution found by the synthesis. This eliminates all tied to the stars of our Galaxy, were determined by optical as- reference to the provisional catalogue H37C which is not rel- trometry following the algorithms outlined in Vondrak´ (1991, evant any more. The given values of the orientation and spin 1996) and Vondrak´ et al. (1992, 1995). Using the preliminary components are the residuals of the individual determinations Hipparcos catalogue H37C, all the latitude/Universal time ob- with respect to the adopted solution. For the orientation com- servations made with 46 instruments at 29 different observa- ponents the residuals refer to the approximate mean epoch of tories all over the world were recalculated into that reference observation of the link observations in question; this epoch is frame. About 3.6 million observations were used to derive EOP also given in Table 3 for the methods providing estimates of ε. at 5-day intervals between 1899.7 and 1992.0. Before describing the methods used for the synthesis and Only the last twelve years of the global solution, common their results, let us make some remarks on the data provided by with VLBI observations (877 different epochs), were then used the various link techniques. to calculate some of the angles and rotations linking the two ce- lestial systems. The methodology and an example is described 4.1. Radio techniques in Vondrak´ (1996). The detailed inspection of the relations be- tween the two sets of EOP (i.e. as observed by optical astrome- The relative precisions provided by the three interferometric try and VLBI) shows that only the celestial pole offsets, which techniques in the determination of the orientation (ε) are con- are completely independent of the terrestrial reference systems sistent with their baseline lengths and are therefore considered used by the two techniques, are fully suitable for determining as realistic. The precision of the determination of the spin (ω) the link. Polar motion is useless for the purpose since it is fully depends both on the basic uncertainty of the observation and of J. Kovalevsky et al.: The Hipparcos Catalogue as a realisation of the extragalactic reference system 629
Table 3. Results of the individual link solutions, expressed as residuals with respect to the adopted solution. The second column contains the abbreviations used to identify the solutions in Fig. 4 and 5. The standard errors supplied with the individual solutions are given in parentheses. The last column gives the approximate mean epoch of the link observations used to determine ε
Method Label Spin components (mas/yr) Orientation components (mas) Epoch ωx ωy ωz εx εy εz 1900+
VLBI VI −0.16 (0.30) −0.17 (0.26) −0.33 (0.30) −0.10 (0.47) +0.08 (0.49) +0.16 (0.50) 91.3 MERLIN ME +1.41(2.60) −0.64(2.20) +0.51(2.40) 94.0 VLA VA +4.27 (4.70) −3.75 (5.30) −5.76 (5.20) 86.3 Hamburg/USNO HP +3.38 (5.00) −0.06 (4.90) −9.20 (4.70) 88.5 HST/FGS ST −1.60 (2.87) −1.92 (1.54) +2.26 (3.42) −6.10 (2.16) −3.25 (1.49) +5.42 (2.14) 94.3 NPM (Heidelberg) LH −0.77 (0.40) +0.15 (0.40) +0.23 (?) NPM (Yale) LY +0.09 (0.18) −0.20 (0.18) +1.46 (?) KSZ Kiev KZ −0.27 (0.80) +0.15 (0.60) −1.07 (0.80) SPM (blue, α)YBA+0.23 (0.13) +0.50 (0.20) 0.00 (0.08) SPM (blue, δ) YBD +0.07 (0.15) +0.58 (0.08) SPM (visual, α)YVA+0.44 (0.12) +0.71 (0.18) −0.30 (0.07) SPM (visual, δ) YVD +0.30 (0.12) +0.76 (0.06) Bonn plates BP +0.93 (0.34) −0.32 (0.25) +0.17 (0.33) Potsdam plates PP +0.22 (0.52) +0.43 (0.50) +0.13 (0.48) EOP EO −0.93 (0.28) −0.32 (0.28) +2.33 (0.88) +7.80 (0.90) 85.0
(?) not used in the synthesis; see Sect. 3.6.1–2 the time span. This gives a major advantage to the VLBI obser- the authors of these methods are small because of the large num- vations both for the orientation and spin. An attempt was made ber of stars, and cannot be considered as realistic. Additional to determine ω with MERLIN observations, but the result was magnitude-related biases certainly exist and this has justified not retained, the time span being notably insufficient. a significant down-weighting of the results provided. The dif- ference between the results obtained at Yale and Heidelberg in 4.2. Optical determination of the orientation their analyses of the NPM1 stars also justifies this policy. It was very important to be able to confirm the radio deter- minations of ε by optical astrometry. The USNO/Hamburg pro- 4.4. Special photographic link programmes gramme which consisted originally of 400 extragalactic sources Relying on archival plates for the first-epoch measurements, was only 20% complete at the time of the link, while the Hub- these programmes are also prone to magnitude equation, with ble Space Telescope observations started very late due to the little possibility to control or study the effect. Because of well-known problems with the telescope. In both cases, the un- this, their formal errors are probably underestimated. Strangely certainties are large, but the methods are promising and would enough, there seems to have been little gain in having a very have given better results with more data. However, the uncer- long time span. Possibly the magnitude-dependent errors are tainties of the HST results seem to be underestimated by the larger or more difficult to model in the old plates, offsetting the formal errors. advantage of the long time baseline.
4.3. Photographic catalogues referred to galaxies 4.5. Earth Orientation Parameters These techniques are much more sensitive to magnitude- dependent errors than the preceding two optical methods. Most In a sense this method is less direct than the others, as it depends of the stars measured in these surveys are faint and comparable on an intermediate (terrestrial) reference frame, whose relations in magnitude with the reference galaxies. But for the link one in the optical and radio domain may not be completely under- had to choose only the brightest of the survey stars, for which stood. Apart from the problem with the z components discussed the effect is likely to be much larger. The magnitude dependence in Sect. 3.11, an additional uncertainty arises from the fact that is not necessarily linear for these bright stars and the link results the mean epoch of observations is 1985 and that all of them depend strongly upon either the model applied or the magnitude were performed before Hipparcos mean epoch. In the synthesis cut-off adopted. This is illustrated by the discussions of Sect. 3.6 method where only ε0 was estimated, this led to a considerable to 3.8 and no result can be considered as being unbiased in this down-weighting of the data. However, even when the strong respect, although the SPM solutions have an advantage in that correlation between ε0 and ω was taken into account, the for- the magnitude equation could be calibrated internally by the mal errors had to be substantially increased to make sense in grating image technique. In any case, the formal errors given by relation to other data. 630 J. Kovalevsky et al.: The Hipparcos Catalogue as a realisation of the extragalactic reference system
ωy +1.0
YVD YVA YBD YBA +0.5 PP
LH KZ 0 ωx
VI LY EO BP -0.5
ST
-1.0 -1.0 -0.50 +0.5 +1.0 mas/yr
ωz +1.0
ST LY
+0.5
LH PP BP 0 ωx YBA
VI YVA -0.5
-1.0 KZ -1.0 -0.50 +0.5 +1.0 mas/yr
Fig. 4. Projections onto the xy and xz planes of the individual solutions Fig. 5. Projections onto the xy and xz planes of the individual solutions for the orientation vector ε (residuals with respect to the adopted vector for the spin vector ω (actually residuals with respect to the adopted at the mean epoch of each solution). The components are expressed in vector). The components are expressed in mas/yr. The solutions are mas. The solutions are labelled as in Table 3 labelled as in Table 3
5. General synthesis of at least some solutions. Different strategies were tried for this down-weighting, including a semi-automatic procedure de- It was decided that the two first authors would proceed indepen- scribed in Sect. 5.2 (Method A). For Method B (Sect. 5.3) the dently to synthesise the observations by different methods (A, down-weighting was essentially based upon the considerations B) and then to compare the results in order to make and justify given in Sect. 4, moderated by the examination of how the mod- the final choice. ifications of the weights affected the goodness-of-fit of the syn- thesised solution and the individual residuals. So, while the 5.1. Individual link data weights deduced from the rms provided by the authors rep- resent essentially formal errors, down weighting takes, at least The results obtained by various individual solutions all included roughly, account of external errors. the values of the components of one or both of the vectors ε0 and ω, together with their estimated standard errors and the associ- 5.2. Method A (L. Lindegren) ated correlation matrix. These data (except the correlations) are summarised in Table 3 in the form of the residuals with respect This method is described in detail in Lindegren & Kovalevsky to the finally adopted solution. (1995) and was strictly followed. As shown in that paper, it is In the synthesis it was found that the individual solutions possible to cast the results of each individual link solution (j) are quite incompatible if the given standard errors were taken at in the form of an information array [ N j hj ] representing the face value. Consequently it was necessary to reduce the weights normal equations N js = hj for the six-dimensional state vec- J. Kovalevsky et al.: The Hipparcos Catalogue as a realisation of the extragalactic reference system 631
0 tor s =[ε0xε0y ε0y ωxωy ωy ]. The full set of correlations correlation matrix, referred to the epoch J1991.25: among the six parameters were taken into account; in particular the correlations between the orientation and spin components ε0x =+0.01 (0.46) mas ε = −0.20 (0.47) mas are important for a uniform treatment of the different mean ob- 0y ε =+0.12 (0.49) mas servation epochs shown in Table 3. 0z , (2) ω =+0.06 (0.16) mas/yr The Heidelberg and Yale analyses of the NPM1 do not rep- x ω = −0.05 (0.15) mas/yr resent independent determinations. They were therefore aver- y ωz =+0.00 (0.14) mas/yr aged prior to the synthesis, and the more pessimistic standard errors from the Heidelberg analysis were adopted for this aver- age. Similarly the blue and visual SPM solutions were averaged, 1+0.25 +0.05 −0.04 −0.01 +0.00 but in this case giving more weight to the blue solutions. Thus, +0.25 1 −0.13 +0.01 −0.11 +0.01 effectively 12 different solutions were considered in the synthe- +0.05 −0.13 1 +0.01 +0.01 −0.06 R sis. The main problem was then to assign a weight wj ≤ 1to = −0.04 +0.01 +0.011+0.05 −0.16 . each of the solutions (corresponding to an increase of its formal −0.01 −0.11 +0.01 +0.05 1 −0.16 −1/2 +0.00 +0.01 −0.06 −0.16 −0.16 1 errors by the factor wj ); this process is described below. Af- ter that, the synthesised solution s, including an estimate of its covariance, could be obtained by solving the normal equations (3) resulting from the sum of the 12 weighted information arrays. The method allows to compute the relative contributions of The determination of the weights w was based on a com- j the various link techniques to the synthesised solution. It turns parison of the goodness-of-fit statistics of the individual so- out that for the orientation parameters, the VLBI observations lutions, q = d0 D+d . Here, d = w h − w N s is the j j j j j j j j j dominate strongly. For the determination of the spin the contri- weighted residual right-hand-side of the normal equations for butions are more evenly spread among the several techniques, solution j and D its covariance; see Eq. (44) in Lindegren j but with the SPM programme and the VLBI observations to- & Kovalevsky (1995). In the absence of biases and if all the gether contributing about half of the total weight. It should be weights are correctly assigned, the expectation of this quantity noted that in this method the MERLIN, VLA, Hamburg/USNO is r = rank(D ), which varies between 2 and 6 for the different j j and HST/FGS links contribute to the determination of the spin link techniques. Note that the generalised inverse D+ was used j components in Eq. (2) by virtue of their spread in observational in the expression for q in order to handle the techniques where j epochs, rather than through their individual determinations of less than all six rotation parameters were determined. The total the spin. goodness-of-fit Q = Σj qj was also computed; its expectation in the ideal situation is R = Σj rj =44. 5.3. Method B (J. Kovalevsky) Starting from some a priori set of weights, the statistics qj and Q were computed. Typically this gave a much too high value This method is based upon the fundamental assumption that the of Q due to unrealistically small standard errors in some of the errors obtained by every task are gaussian. This means that the individual solutions. The most discrepant solution was identi- probability density function (PDF) is given in its most general fied by comparing the normalised statistics qj/rj, the weight of form for n variables by that solution was halved, and a new synthesised solution was 1 computed with revised qj and Q. This process was iterated until f(x ,x , ..., x )= × 1 2 n (2 )n/2 V 1/2 Q ' R and all qj ' rj. π | | n n It is not obvious that this semi-automatic process of down- 1 − × exp − V 1 (x − x )(x − x ) . (4) weighting converges to a unique result. Indeed, slightly different 2 ik i i k k " i=1 k=1 # weights were obtained depending on whether the formal stan- X X dard errors were taken as the starting point (i.e. wj = 1 for all where V is the variance-covariance matrix of the variables and j initially) or some a priori judgement of the relative weights xi their mean values. were first applied. However, the synthesised solutions resulting This PDF can be computed from the data provided by each from such experiments rarely differed by more than 0.1 mas and individual link task (j), namely the estimated variables with 0.1 mas/yr, and the final result was not very sensitive to addi- their standard errors and the correlation matrix. Now, the joint tional changes in the weights. Independent of the starting point, PDF of J gaussian distributions is the product of the PDFs of it was found that the solutions from the SPM programme and the these distributions, Earth orientation parameters had to be severely down-weighted, and the Bonn and HST solutions slightly down-weighted, but J otherwise the given standard errors were roughly consistent with ϕ = fj(x1,x2, ..., xn), (5) =1 the overall solution. Yj The results of Method A are summarised by the following which is easily computed, and has exactly the same form as rotation parameters (with standard errors in parentheses) and Eq. (4) since the quantities in the exponential add. One can 632 J. Kovalevsky et al.: The Hipparcos Catalogue as a realisation of the extragalactic reference system therefore compute back the variance-covariance matrix corre- B2. Solution using only ω as the unknown: the weighted sponding to ϕ and derive the standard errors and the correlations rms residual was 0.3 mas/yr. The solution vector and correlation of the merged solution. This approach explicitly assumes gaus- matrix were sian error distributions and it would not be correct to apply it ω = −0.01 (0.13) mas/yr to other distributions. However, in the particular case to which x ω =+0.08 (0.13) mas/yr , (8) it is applied, no indication of a non-gaussian behaviour was y ω = −0.05 (0.18) mas/yr given by the individual link solutions which all made the same z assumption. Although formulated in a probabilistic framework, this 1+0.04 −0.11 method is in principle equivalent to a weighted least-squares and R = +0.04 1 −0.14 . (9) should yield similar results as Method A. However, the practical à −0.11 −0.14 1 ! implementations differ, and Method B was also applied sepa- B3. Solution using both ε (referred to J1991.25) and ω rately to the spin and orientation components, which may add 0 as unknowns: the weighted rms residual was 1.2 mas for the some insight into the properties of the individual solutions. As orientation components and 0.4 mas/yr for the spin components. in Method A, a main problem is to adjust the relative weights The solution vectors and correlation matrix were of the contributing solutions. To begin with, the four solutions obtained from the Yale ε0x=+0.16 (0.41) mas SPM programme were reduced into a single one by taking a ε0y =+0.18 (0.43) mas ω weighted mean. The MERLIN and HST results for were not ε0z =−0.06 (0.46) mas , (10) used because of their large uncertainties. ωx =−0.06 (0.08) mas/yr In a first approximation, an unweighted solution for ε0 and ωy =+0.05 (0.09) mas/yr ω another solution for were computed neglecting the correla- ωz =0.00 (0.14) mas/yr tions between these quantities. This is justified because they are close to zero in the case of the most accurate method (VLBI), 1+0.05 +0.00 +0.24 +0.08 −0.01 but less justified for the EOP method in which the correlations +0.05 1 −0.13 +0.06 +0.10 −0.01 are about 0.89, but in this case the uncertainties are also much +0.00 −0.13 1 −0.02 −0.02 +0.00 larger. R = . +0.24 +0.06 −0.02 1 −0.13 −0.05 In further iterations weights were modified progressively in +0.08 +0.10 −0.02 −0.13 1 −0.12 order to reduce the largest residuals and the overall goodness- −0.01 −0.01 +0.00 −0.05 −0.12 1 2 of-fit, as measured by the χ statistic. No systematic procedure (11) was used to modify the weights, but rather a successive approx- imation technique with steps of 0.2 in the weights. The correlations obtained in solutions B1 and B2 agree rather Essentially, the Lick results were strongly down-weighted well with those obtained from Method A, while the correlations as actually it was suggested already by the authors, the formal er- in B3 deviate somewhat. However, the correlations are in all rors being abnormally small. Both HST and Earth Rotation were cases small or only moderately large, showing that the combi- also strongly down-weighted, and Bonn results also somewhat nation of link solutions gives a well-conditioned determination down-weighted while both Potsdam and Kiev results had their of all the parameters at the central epoch of the Hipparcos Cat- weight slightly increased. Globally, this confirms the weights alogue. obtained in method A. Then, a global solution taking as unknowns all the six pa- 6. Final results rameters of ε0 and ω and starting with the weights obtained in the preceding solutions. This did not change significantly the re- After a comparison of these results and their discussion, it ap- sults, as can be seen from the following summary of the different peared that a mean value of the two methods should be consid- solutions. ered as the final solution for the link. The adopted orientation B1. Solution using only ε0 (referred to J1991.25) as the un- and rotation vectors correspond to all parameters equal to zero, known: the weighted rms residual was 0.8 mas. The solution which is close to a mean value of A and B3. The standard er- vector (with standard errors in parentheses) and correlation ma- rors of the parameters were estimated to be 0.6 mas in each of trix were the components of ε0, and 0.25 mas/yr in the components of ω. These numbers were obtained by a conservative rounding ε0x =0.00 (0.51) mas of the formal errors resulting from the synthesis, taking into ε = −0.04 (0.51) mas , (6) 0y account also the spread of values obtained in the different syn- ε0z =+0.16 (0.53) mas thesis solutions and the uncertainty in the relative weights of the different link techniques. It is to be noted that this link will 1+0.28 −0.01 become worse as time goes on. It is important that, in the fu- R = +0.28 1 −0.14 . (7) ture, new ground-based observations be organised to maintain à −0.01 −0.14 1 ! and possibly improve the quality of the link. J. Kovalevsky et al.: The Hipparcos Catalogue as a realisation of the extragalactic reference system 633
Acknowledgements. This work is based on a world-wide coopera- IERS, 1996, 1995 Annual report, Observatoire de Paris tion of agencies, institutes and individuals. It is based on observa- Jefferys W.H., 1962, AJ 67, 532 tions with the Hipparcos satellite built and operated by the European Jefferys W.H., Fitzpatrick M.J., McArthur B.E., McCartney J.E., 1988, Space Agency, the NASA/ESA Hubble Space Telescope operated by GaussFit: A System for Least Squares and Robust Estimation, Univ. AURA Inc under a NASA contract, the NASA Deep Space Network, of Texas, Austin the US and European VLBI Networks, the NRAO Very Large Base- Johnston K.J., Fey A.L., Zacharias N., et al., 1995, AJ 110, 880 line Array and VLA operated by Associated Universities Inc (NST Kharchenko N.V., Schilbach E., Scholz R.-D., 1994, Astron. Nachr. contract), and the participation of the CNES computing centre. The 315, 291 support of these agencies is gratefully acknowledged. MERLIN is a Kharchenko N.V., Schilbach E., 1995, Astron. Nachr. 316, 91 UK national facility operated by the University of Manchester on be- Kislyuk V.S.,Rybka S.P.,Yatsenko A.I., Kharchenko N.V.,1997, A&A half of the Particle Physics and Astronomy Research Council. The 321, 660 compilation and distribution of preliminary Hipparcos data was done Klemola A.R., Jones B.F., Hanson R.B., 1987, AJ 94, 501 by H. Schrijver (SRON, Utrecht) and D. Morin (Observatoire de Paris) Klemola A.R., Hanson R.B., Jones B.F., 1994, Lick NPM program: based on the results of the Hipparcos data reduction consortia FAST and NPM1 Catalog and its applications, in: Morrison L.V.,Gilmore G.F. NDAC. P. Hemenway acknowledges several grants from NASA the (eds.) Galactic and Solar System Optical Astrometry. Cambridge last being NASA Grant NAGW/3111. J. Kovalevsky and J-F. Lestrade University Press, p. 20 acknowledge financial support by CNES and Centre National de la Kovalevsky J., Falin J.L., Pieplu J.L., et al., 1992, A&A 258, 7 Recherche Scientifique (CNRS). L. Lindegren acknowledges financial Lindegren L., Kovalevsky J., 1995, A&A 304, 189 support from the Swedish National Space Board. I. Platais acknowl- Lindegren L., Høg E., van Leeuwen F., et al., 1992, A&A 258, 18 edges the support of the US National Science Foundation for the SPM Lestrade J.-F., Jones D.L., Preston R.A., et al., 1995, A&A 304, 182 programme through grants to Yale University and the Yale Southern Ma C., Arias E.F., Eubanks T.M., Fey A.L., Gontier A.M., Jacobs, C.S., Observatory Inc. H.-J. Tucholke and P. Brosche acknowledge finan- 1997, IERS Technicalnote 23, Observatoire de Paris cial support from the Bundesministerium fur¨ Forschung und Tech- Ma C., Shaffer D.B., de Vegt C., Johnston K.J., Russel J.L., 1990, AJ nologie (FKZ 50 00 9101). C. de Vegt acknowledges financial support 99, 1284 from Bundesministerium fur¨ Forschung und Technologie under grant Pan X., Shao M., Colavita M.M., 1993, ApJ 413, L129 No. 50008810. J. Vondrak´ acknowledges the grants 205/95/0062 of Perryman M.A.C., Høg E., Kovalevsky J., et al., 1992, A&A 258, 1 the Grant Agency of the Czech Republic and A3003502 of the Czech Platais I., Girard T.M., van Altena W.F., et al., 1995, A&A 304, 141 Academy of Sciences. Rybka S.P., Yatsenko A.I., 1997, A&AS 121, 243 Scholz R.-D., Kharchenko N.V., 1994, Astron. Nachr. 315, 73 Thomasson P., 1986, QJRAS 27, 413 References Tucholke H.-J., Brosche P., Odenkirchen M., 1997, A&AS 122, 433 Argue A.N., 1989, The link to extragalactic objects, in: Perryman et al. Turon C., Gomez´ A., Crifo F., et al., 1992, A&A 258, 74 (eds.) The Hipparcos Mission, ESA SP-1111, Volume II (The Input van Altena W.F., Girard T., Lopez´ C.E., Lopez´ J.A., Molina E., 1990, Catalogue), p. 199 The Yale-San Juan Southern Proper Motion program (SPM), in: Argue A.N., 1991, Hipparcos: Its link to an extragalactic reference Lieske J.H., Abalakin V.K. (eds.) Proc. IAU Symp. 141, Inertial frame, in: Hughes J.A., Smith C.A., Kaplan G.H. (eds.) Proc. IAU coordinate system on the sky. Kluwer, Dordrecht, p. 419 Coll. 127, Reference Systems. US Naval Observatory, Washington de Vegt C., Gehlich U.K., 1982, A&A 113, 213 D.C., p. 63 Vondrak´ J., 1991, Bull. Astron. Inst. Czechosl. 42, 283 Arias E.F., Charlot P., Feissel M., Lestrade J.-F., 1995, A&A 303, 604 Vondrak,´ J., 1996, Indirect linking of the Hipparcos catalog to ex- Benedict G.F., Nelan E., Story D., et al., 1992, PASP 104, 958 tragalactic reference frame via Earth orientation parameters, in: Bergeron J., 1991, IAU Transactions, Vol. XXIB, Kluwer, Dordrecht, Ferraz-Mello S., Morando B, Arlot J.E. (eds.) Proc. IAU Symp. p. 41 172, Dynamics, ephemerides and astrometry in the solar system. Clark B.G., 1980, A&A 89, 377 Kluwer, Dordrecht, 491 Dick W.R., Ruben G., Schilbach E., Scholz R.-D., 1987, Astron. Nachr. Vondrak´ J., Feissel M., Essa¨ıfi N., 1992, A&A 262, 329 308, 211 Vondrak´ J., Ron C., Pesekˇ I., Cepekˇ A., 1995, A&A 297, 899 ESA, 1997, The Hipparcos Catalogue, to appear as ESA SP-1200 Vondrak´ J., Ron C., Pesekˇ I., 1997, A&A 319, 1020 Florkowski D.R., Johnston K.J., Wade C.M., de Vegt C., 1985, AJ 90, Zacharias N., de Vegt C. et al., 1995, AJ 110, 3093 2381 Frœschle,´ M., Kovalevsky, J., 1982, A&A 116, 89 Garrington S.T., Davis R.J., Morrison L.V.,Argyle R.W.,1997, Linking radio and optical frames with MERLIN, in preparation Geffert M., Klemola A.R., Hiesgen M., Schmoll J., 1997, Absolute proper motions for the calibration of the Hipparcos proper motion system, submitted to A&A Ghez A.M., Neugebauer G., Matthews K., 1993, AJ 106, 2005 Girard T.M., Platais I., Kozhurina-Platais V., van Altena W.F., 1997, in preparation Hirte S., Schilbach E., Scholz R.-D., 1996, The Potsdam contribution to the extragalactic link of the Hipparcos proper motion system, a A&AS, in press This article was processed by the author using Springer-Verlag LTEX Høg E., Bastian U., Egret D., et al., 1992, A&A 258, 177 A&A style file L-AA version 3.